All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We have already issued Fataawa 83877 and 83600 clarifying the ruling on Tasbeeh prayer. As regards the supplication of Gunjul Arsh, we are not aware of any supplication with this name in the Sunnah. It would have been better if you had mentioned to us this supplication so that we may investigate whether or not it is confirmed in the Sunnah with another name, and if it is not confirmed, we will find out whether or not it contains any religious prohibitions.
With regard to whether you should preoccupy yourself with the memorization of the Quran or perform Tahajjud prayer, then both are good acts of worship, and if you can combine between them, it would be better. If it is not possible to combine between both of them in one night, then you should reserve one night for the memorization of the Quran and one night for Tahajjud, and you should perform the prayer while reciting the verses which you had memorized. Reciting the Quran in the night prayer is the best way of making firm your memorization of it.
Finally, we draw your attention to the importance of making sure that your recitation of the verses which you want to memorize is correct, by reciting them to a competent Shaykh [who would correct you] before starting to memorize so that you would not memorize the Quran in a wrong manner.
Allaah Knows best.